The authors make another claim:
STRUCTURE cannot distinguish recent admixture from a cline of other origin, and these analyses cannot prove admixture in the Uyghurs; however, historical records indicate that the present Uyghurs were formed by admixture between Tocharians from the west and Orkhon Uyghurs (Wugusi-Huihu, according to present Chinese pronunciation) from the east in the 8th century CE.14 The Uyghur Empire was originally located in Mongolia and conquered the Tocharian tribes in Xinjiang. Tocharians such as Kroran have been shown by archaeological findings to appear phenotypically similar to northern Europeans,15 whereas the Orkhon Uyghur people were clearly Mongolians. The two groups of people subsequently mixed in Xinjiang to become one population, the present Uyghurs. We do not know the genetic constitution of the Tocharians, but if they were similar to western Siberians, such as the Khanty, admixture would already be biased toward similarity with East Asian populations.First of all, the authors forget about the eastern Iranian peoples (Sakas) who most surely were present among the ancestors of the Uyghurs. Second, there is no reason to think that Tocharians were similar to the Khanty, a population with a substantial presence of northern Eurasian Y-haplogroup N does not make a link with Uyghurs likely.
Am J Hum Genet. 2009 December 11; 85(6): 934–937.
Genetic Landscape of Eurasia and “Admixture” in Uyghurs
Hui Li et al.